I. Begin with the highest denomination and divide as in simple numbers:

II. Reduce the remainder, if any, to the next lower denomination and add in the units of that denomination, for a new dividend:

III. Proceed in the same manner, through all the denominations.

PROOF.-By multiplication, as in simple numbers.

NOTES.-1. If the divisor is a composite number, we may divide by the factors in succession, as in simple numbers.

2. Each quotient figure has the same unit as the dividend from which it was derived.

3. If the divisor is a denominate number, reduce it and the dividend to the same unit, and then divide as in simple numbers.

5. Divide 17 cwt. 0 qr. 2 lb. 6 oz. by 7.

6. Divide 49 yd. 3 qr. 3 na. by 9.

7. If a man, lifting 8 times as much as a boy, can raise 201 lb. 12 oz., how much can the boy lift?

8. If a vessel sails 25° 42′ 40′′ in 10 days, how far will she sail in one day?

9. Divide 9 hhd. 28 gal. 2 qt. by 12.

10. What is the quotient of 65 bu. 1 pk. 3 qt. divided by 12?

11. In 4 equal packages of medicine, there are 13 tb 73 23 1 4 gr.: how much is there in each package?

12. In 9 fields there are 113 A. 3 R. 25 P. of land: if the fields contain an equal amount, how much is there in each field?

13. If 15 loads of hay contain 35 T. 5 cwt., what is the weight of each load?

14. In 25 hhd. of molasses, the leakage has reduced the whole amount to 1534 gal. 1 qt. 1 pt.: if the same quantity has leaked out of each hogshead, how much will each hogshead still contain?

15. Bought 65 yards of cloth, for which I paid £72 14s. 41d. what did it cost per yard?

:

16. £1138 12s. 4d. 53. | 18. 70 T. 17 cwt. 7 lb. ÷ 79. 17. 27 bu. 7 qt. ÷ 84.

19. 114 hhd. 56 gal. 1 qt. ÷ 40.

20. If, in 30 days, a man travels 746 mi. 5 fur., traveling the same distance each day, what is the length of each day's iourney?

21. Suppose a man had 98 lb. 2 oz. 19 pwt. 5 gr. of silver how much must he give to each of 7 men, if he divides it equally among them?

22. When 175 gal. 2 qt. of beer are drank in 52 weeks, how much is consumed in one week?

219. What is Division of Compound Numbers? Give the rule for division. How do you prove division? How do you divide, when the divisor is a composite number? What will be the unit of each quotient figure?

Applications in the foregoing Rules.

1. A farmer has 18 lots, each of which contains 41 A. 2 R. 11 P.; these are divided among his 7 children: how much does each child have?

2. A rich man divided 168 bu. 1 pk. 6 qt. of corn, among 35 poor men: how much did each receive?

3. There are three men, the sum of whose ages is 14 times 20 yr. 5 mo. 3 wk. 6 da.: if the ages are equal, what is the age of each ?

4. In sixty-three barrels of sugar, there are 7 T. 16 cwt. 3 qr. 12 lb.: how much is there in each barrel?

5. One hundred and seventy-six men consumed, in a week, 13 cwt. 2 qr. 15 lb. 6 oz. of bread: how much did each man consume in 1 day?

6. If the earth revolves on its axis 15° in 1 hour, how far does it revolve in 1 minute?

7. A farmer has a granary containing 232 bushels 3 pecks 7 quarts of wheat, and he wishes to put it in 105 bags: how much must each bag contain?

8. If 59 casks contain 44 hhd. 53 gal. 2 qt. I pt. of wine, what are the contents of of a cask?

9. Bought 90 hhd. of sugar, each weighing 12 cwt. 2 qr. 14 lb. what is the value of the sugar, at 64 cents per lb.? 10. If 90 hogsheads of sugar weigh 56 T. 14 cwt. 3 qr. 15 lb., what is the weight of 1 hogshead?

11. If a vessel sails 30 days, at the rate of 49 mi. 6 fur. 8 rd. per day, at what rate per day does another ship sail, that performs the same voyage in 12 days?

12. Divide £18 6s. 9d. by £4 9s. 3d.

NOTE.-Reduce both quantities to pence, and then divide.

13. A steamship, in crossing the Atlantic, has a distance of 3500 miles to go: if she sails 211 mi. 4 fur. 32 rd. a day, what distance, after 15 days, has she still to sail?

14. A printer uses one sheet of paper for every 16 pages of an octavo book: how much paper will be necessary to

print 500 copies of a book containing 336 pages, allowing 2 quires of waste paper in each ream?

15. How many barrels of sugar, containing 2 cwt. 1 qr. 15 lb., can be filled from a hogshead of 1 T. 5 cwt. 2 qr. 20 lb.?

16. A man lends his neighbor £135 6s. 8d., and takes in part payment, 4 cows, at £5 8s. apiece, also a horse, worth £50: how much remained due?

17. If a man travels 24 mi. 7 fur. 30 rd. in a day, how long will it take him to travel 200 mi. 6 fur. 18 rd.?

18. Out of a pipe of wine, a merchant draws 12 bottles, each containing 1 pint 3 gills; he then fills six 5-gallon demijohns; then he draws off 3 dozen bottles, each containing 1 quart 2 gills: how much remained in the cask?

19. If a barrel of flour costs £1 4s. 9d., how many barrels can be bought for £275 10s. 6d. ?

20. Suppose a man has 246 mi. 6 fur. 36 rd. to travel in 12 days after traveling 9 days, how far has he yet to travel?

21. A vessel arrives in port, with a cargo of 50 hogsheads of sugar, each containing 1 T. 5 cwt. 3 qr.; 40 hogsheads, each containing 18 cwt. 2 qr. 12 lb., and 75 hhd., each containing 15 cwt. 3 qr. 18 lb.: 8 merchants buy the entire cargo: what amount of sugar belongs to each?

22. A ship, with a cargo of 250 bales of cotton, each weighing 12 cwt. 2 qr. 15 lb., was overtaken by a storm, and obliged to throw overboard 60 bales; the cotton was owned in equal shares, by 5 merchants: what was the loss to each, at 25 cents per lb, and what quantity did each receive?

23. How many pieces of cloth, each containing 35 yards, will clothe a company of 48 men, if it takes 5 yd. 3 qr. 2 na. for each man?

24. A merchant bought 15 pieces of cloth, 3 of which contained each 34 yd. 3 qr.; 6 contained each 37 yd. 1 qr. 3 na., and the remainder, 40 yd. 24 qr. each: allowing 2 yd. 3 qr. for waste, how many suits, each requiring 6 yd. 1 qr. 3 na., can be made from the cloth?

LONGITUDE AND TIME.

220. The Equatorial Circumference of the Earth is divided into 360°, which are called degrees of Longitude.

221. The Sun apparently goes round the earth once in 24 hours. This time is called a day. Hence, in 24 hours, the sun apparently passes over 360° of longitude; and in 1 hour, over of 360° 15°.

222. Since the sun, in passing over 15° of longitude, requires 1 hour, or 60 minutes of time, in 1 minute of time he will pass over of 15° = 15′ of longitude; and in 1 second of time, over of 15' =

longitude: Hence,

15° of longitude require

=° =

60

1. If the longitude, expressed in degrees, minutes, and seconds, be divided by 15 = 3 × 5, the quotients will be hours, minutes, and seconds of time.

2. If time, expressed in hours, minutes, and seconds, be multiplied by 15 = 3 × 5, the product will be degrees, minutes, and seconds of longitude.

223. When the sun is on the meridian of any place, it is 12 o'clock, or noon, at that place.

Now, as the sun apparently goes from east to west, at the instant of noon, at one place, it will be past noon for all

220. How is the circumference of the earth supposed to be di vided?

221. How does the sun appear to move? What is a day? How far does the sun appear to move in 1 hour?

222. How do you reduce degrees of longitude to time? How do you reduce minutes of longitude to time? How do you reduce seconds to time? How do you reduce time to longitude?